SOLUTION: Please help me solve this exercise; The directions are, write an equation for each. Passes through (4,10) and is perpendicular to the line 6x-3y=5. I have tried midpoint an

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Question 182916This question is from textbook
: Please help me solve this exercise;
The directions are, write an equation for each.
Passes through (4,10) and is perpendicular to the line 6x-3y=5.
I have tried midpoint and point slope formula and I am still stuck.
Look forward to hearing from you. This question is from textbook

Found 2 solutions by nerdybill, solver91311:
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
Start by putting:
6x-3y=5
into the "slope-intercept" form:
y = mx + b
where
m is slope
b is y-intercept
.
6x-3y=5
-3y = -6x + 5
y = 2x - 5/3
So, now we know that the slope of this line is 2
.
If we want, a line that is perpendicular to the above, the slope has to be the "negative reciprocal"
So, our NEW line has to have a slope of -1/2 because:
2(-1/2) = -1
.
Recapping we have:
m = -1/2
and a single point at (4,10)
.
Stuff it all into the "point-slope" form:
y - y1 = m(x-x1)
y - 10 = (-1/2)(x-4)
y - 10 = (-1/2)x + 2
y = (-1/2)x + 12 (this is what they're looking for)

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Given a point on a line and the slope of the line, you can determine the equation of the line using the point-slope form:

Where m is the slope, and are the coordinates of the given point.

The slopes of perpendicular lines are negative reciprocals, that is:

So, take your given equation, solve for y to put it into slope intercept form:

The slope of the given line will be the coefficient on the x term. Take the negative reciprocal (invert the fraction and put a minus sign in front of it) of that slope and with the given point you will have enough information to use the point-slope form to derive your required equation.

John